Structure Design and Modelling of an Origami-Inspired Pneumatic Solar Tracking System For

IAC-15-D1.1.7

STRUCTURE DESIGN AND MODELLING OF AN ORIGAMI-INSPIRED PNEUMATIC SOLAR TRACKING SYSTEM FOR NPU-PHONESAT

Qiao Qiao

National Key Laboratory of Astronautics Flight Dynamics, China

Northwestern Polytechnical University, China,

Jianping Yuan

National Key Laboratory of Astronautics Flight Dynamics, China

Northwestern Polytechnical University, China,

Xin Ning

National Key Laboratory of Astronautics Flight Dynamics, China

Northwestern Polytechnical University, China,

Various plants have the ability to follow the sun with their flowers or leaves via a mechanism known as heliotropism, which is characterized by pressure gradients between neighboring motor cells. By adapting this bio-inspired mechanism, in this paper, we present a novel origami-inspired pneumatic solar tracking system for NPU-PhoneSat, which is capable of achieving the omnidirectional tracking without altering the attitude of the NPU-PhoneSat. This paper gives an overview of the system design, as well as addressing the theoretical modeling problem of the origami-inspired pneumatic solar tracking system. In addition, this paper provides a set of systematic design rules which provide insight into the influence of geometrical parameters on the performance of the system. Such an understanding of soft solar trackers will allow their performance predicted, thus enabling their wide application in enhancing energy supply for small satellites.

I. INTRODUCTION

In recent years, small satellites, such as nanosatellites and picosatellites, have received great attention due to their low cost, short development lifecycle and promising applications.[1-3] Sufficient power supply is a typically demanding factor for the high performance of small satellites. However, due to the limited surface area of small-sized spacecraft, body-mounted solar cells are incapable of providing enough power for onboard instruments. Hence, deployment of large solar arrays has been adopted as an efficient on-board power generation solution without substantially increasing the volume of the satellite.[4] Nevertheless, the solar power collection efficiency is rather low if the angle between the solar array and sunlight is small.

In order to enhance the solar irradiation absorbed by the solar array, we looked to develop a solar tracking system that tracks the sun and keeps the sun’ rays almost perpendicular to the plane of the solar system, mimicking the behavior of certain flowers which follow the sun during the day.[5] The existence of a solar tracking system is not essential for the operation of solar arrays, but without it, performance of solar energy collection is reduced.[6] Equipped with the solar tracking system, small satellites could maintain task-required attitude while maximizing the solar electric energy generation. There are basically two kinds of tracking system, single-axis[7-11] and dual-axis[12-14]. However, these solar tracking systems usually comprise many rigid parts, such as gears and motors, making them large and heavy. Considering the typical volume, mass and cost constraints imposed by the small-sized satellites, these disadvantages make any kind of tracking system prohibitive.

In order to develop a solar tracking system for small satellite which is inexpensive, simple to fabricate, light in weight and compact in packaging state, we expect to harness the intrinsic mechanical properties of folded structures. Known as the traditional Chinese art, origami has inspired plenty of fascinating designs, such as actuators[15] and springs[16]. The power of origami in designing entire robotic platforms has been discovered in [17-21]. In this paper, we identify the characteristic of continuous bending of origami and use them as structure elements in designing solar tracking system.

In this paper, we demonstrate an origami-inspired solar tracking system that is activated by pressurized air, which is specially designed for a foldable picosatellite called NPU-PhoneSat.[22] The solar tracking system is constructed from a combination of elastomeric materials and origami structure[23], which is capable of pointing the solar array towards the sun continuously, thereby ensuring the power supply of the NPU-PhoneSat. While origami-inspired system has received significant research attention, limited modeling work has been conducted. To get a deeper insight into the response of the soft solar tracking system, theoretical model of the pneumatic origami-inspired solar tracker is proposed. This paper is organized as follows: The second section describes the design of the origami-inspired solar tracking system and the third section addresses the theoretical modeling of it. Finally, the influence of geometrical parameters on the response of the solar tracker obtained from the analytical model is presented followed by a conclusions section.

II. DESIGN

The folding pattern we use in our design for the solar tracking system is shown in Figure 1, where valley and mountain folds are indicated by dashed and solid lines, respectively. The Yoshimura pattern shown in Figure 1 is named after a scientist who observed the buckling of a thin cylindrical shell under axial compression.[24] The origami structure folded from the buckling pattern is extremely useful in generating continuous bending, as it possess the characteristics similar to that of springs.

Figure 1: Yoshimura pattern with its respective semifolded shape. In this sketch, mountain folds and valley folds are indicated by dashed lines and solid lines, respectively.

The actuation of the origami mechanism requires powerful and effective methods. Considering the volume and mass constraints of small satellites, pneumatic actuation would be a promising candidate because their lightweight, high power-to-weight ratio and low material cost. Embedding origami structures in elastomeric polymers makes it possible to fabricate soft pneumatic system. Figure 2 details the fabrication process of the origami-inspired solar tracking system. To fabricate this mechanism, the origami structure folded from the Yoshimura pattern was first inserted into the cylindrical mold, and a round rod was used to define the interior shape of the origami structure. Then the elastomer pre-mixture was poured into the mold and cured with the origami structure embedded.

Figure 2: Fabrication process of the origami-inspired solar tracker. (a) The origami structure folded from the Yoshimura pattern; (b) the origami structure inserted in the cylindrical mold with elastomer pre-mixture poured and cured; (c) origami structure with elastomeric polymer covered.

For ease of storage and transportation, the origami-inspired solar tracking system is in the compact folded state during launch (Figure 3 (a)). After launch, the inflation powders inside the pneumatic channel sublimate, resulting in the semi-unfolded state of the solar tracking system (Figure 3 (b)). In order to achieve the omnidirectional tracking without altering the attitude of the NPU-PhoneSat, corresponding longitudinal pneumatic channel is pressurized through heating the gas inside it, thus achieving the continuous bending of the solar tracking system in all direction. The functionality of the origami structure is similar to that of the hinge, as well as providing structure support. The specific attitude of solar array is achieved through the selection of the longitudinal pneumatic channel on the circumference and control of the temperature inside it.

Figure 3: (a) Folded state of the solar tracker during launch. (b) Semi-unfolded state. (c) Bending state when pressurized.

III. MODEL

In order to predict the response of the origami-inspired solar tracking system when pressurized, theoretical model is developed and the relationship between the input air pressure and the bending angle is established. The development of the model takes into consideration both the property of the elastic material and the geometry of the origami structure. It is assumed that when the pressure in the longitudinal pneumatic channel increased, the elastic material covering the corresponding pneumatic channel extends while the other side is constrained by the extensible material not stretched, thus causing the solar tracking system to bend (Figure 3c). It is assumed that the bending curvature of the soft solar tracker is always uniform when pressurized.

When the solar tracker reaches a certain bending configuration in response to the increase in the pressure in the longitudinal pneumatic channel, torque equilibrium was reached where the moment actuating the bending and the resisting bending moment are equivalent, which is the basis for the derivation of the relationship between the input air pressure and the bending angle. The torque equilibrium can be written as follows,

[1]

where is the moment actuating the bending and represents the resisting bending moment.

It is obvious that the moment actuating the bending is supplied completely by the internal air pressure against the origami structure. Due to the symmetry of the origami structure, as shown in Figure 4, only the internal air pressure against the topmost triangle of the origami structure produces effective actuating moment. According to Figure 5, the actuating moment caused by the internal air pressure can be calculated as

[2]

where a and are the side length and angle of the isosceles triangle, respectively.

Figure 4: Sketch of the pressure in the pneumatic channel.

Figure 5: Sketch of the topmost triangle of the origami structure for calculating the actuating moment caused by the internal air pressure.

Furthermore, there are two factors contributing to the resisting bending moment : the opposing bending moment caused by the stresses acting on the outer extensible elastic material and the resisting moment generated by the spring-like origami when bending, that is

[3]

(A) Resisting moment caused by the stretch of the elastic material

As can be seen in Figure 6, when the soft solar tracker bend with a radius R and angle θ, the angle of the bending element can be derived from the geometrical configuration of the origami structure. The relationship between the total bending angle of the solar tracker θ and the central angle related to the bending element can be written as

[4]

where represents the number of replication of the origami structure. Moreover, according to the geometric relationship, the relationship between the central angle related to the bending element and the angle of the bending element can be calculated as

[5]

Figure 6: The geometric relationship between the total bending angle and the angle of the bending element.

In order to calculate the opposing bending moment induced by the stress in the extensible material, the elastic material covering the pneumatic channel is modeled as planar triangle with a certain thickness, as shown in Figure 7. For the sake of simplicity, only a half of the covering material of the bending element is illustrated in Figure 7. According to the geometric relationship indicated in Figure 7, we can have

[6]

[7]

[8]

[9]

[10]

Accordingly, the resisting bending moment induced by the stretch in the elastic material can be calculated as

[11]

where is the longitudinal stress of the elastic material and t is the thickness of the elastic material. According to [26], the longitudinal stain and stress can be calculated as

[12]

[13]

Figure 7: Resisting moment caused by the stress in elastic material. (a) Closeup view of the bending element with half covering elastic material. (b) Sketch of the A-A’ cross section.

(B) Resisting moment caused by the bending of the origami structure

The bending of the origami structure is similar to that of the spring. Consequently, the resisting moment caused by the origami structure when bending could be approximated by the model of the spring. It is assumed that the spring is uniform, thus with the total bending angle being θ under the external bending moment , the bending angle of each circle is , similar to that of the bending element in the origami structure. It is evident that the resisting moment of the spring is equal to the external bending moment when reaches the moment-equilibrium. The deformation element of the spring is illustrated in Figure 8. The moment in the cross section of the spring is equal to the external bending moment, i.e. resisting moment caused by bending. Since the work done by the external moment is equivalent to the stain energy stored in the rod, the relationship between the bending angle and the resisting moment can be derived as[25]

[14]

where l is the length of the rod, G is the elastic modulus of the material and is the polar moment of inertia of the cross section.

Figure 8: Sketch of the deformation element of the spring.

Substituting Equation (2)-(14) into (1), a relationship between the internal air pressure and the bending angleθ can be obtained.

IV. SIMULATION

(a)

(b)

Figure 9: Analytical results for the solar tracking system in free space at 30 degrees, 60 degrees and 90 degrees. (a) Pressure versus system length. (b) Pressure versus wall thickness of the elastic material.

In order to demonstrate the value of the proposed theoretical model of the solar tracking system, several geometrical parameters (i.e. length and wall thickness) are varied to investigate their influence on the bending angle of 30 degrees, 60 degrees and 90 degrees. As shown in Figure 9, the length of the solar tracker is varied while the wall thickness is keep constant in order to demonstrate the influence of geometry, and the effect of wall thickness is studied in the same way. Specifically, Figure 9 (a) demonstrates the results of the pressure versus length of the solar tracking system, for length ranging from 0.05m to 0.15m. As we can see from the figure, for an increase in the length, lower pressure is required to achieve the bending. Similarly, pressure versus wall thickness of the elastic material is shown in Figure 9 (b), with the wall thickness ranging from 1mm to 1cm. As the wall thickness increased, the pressure required to achieve the specific bending angle has also to increase.

V. CONCLUTION

This paper presents a novel design of origami-inspired pneumatic solar tracking system for NPU-PhoneSat, which is capable of achieving the omnidirectional tracking without altering the attitude of the NPU-PhoneSat. An overview of the system design is detailed. In contrast to the traditional solar tracking system, the proposed origami-inspired pneumatic solar tracking system is inexpensive, simple to fabricate, light in weight and compact in packaging state. In order to predict the solar tracker’s performance prior to manufacture, the theoretical model of the solar tracking system is provided establishing explicit relationships between interior pressure and bending angle. Furthermore, to get a deeper insight into the response of the soft solar tracking system, the influence of geometrical parameters on the performance of the solar tracker is also investigated.

There are still some issues that need to be resolved in the future. Experiments of the proposed solar tracking system will be performed, in order to demonstrate the validity and accuracy of the proposed analytical models. In addition, the analysis of the dynamic behavior of the origami-inspired solar tracker should also be implemented in the future.

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